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Topic: Apollo 8 mission insignia v. actual flight profile
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Paul78zephyr Member Posts: 678 From: Hudson, MA Registered: Jul 2005
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posted 12-12-2007 09:33 PM
It is my understanding that the Apollo 8 mission insignia was originally, and very cleverly, 'penned' by Jim Lovell upon his hearing that Apollo 8 (his next mission) would be a translunar mission.What I want to know, though, is did the Apollo missions actually fly a 'figure 8' type trajectory to the moon and back? My understanding is that practically all launches into Earth orbit launch in a west-to-east direction to take advantage of the Earth's axial rotational motion. If one were to look down at the Earth and moon from a fixed point in space from above the Earth's north pole one would see two spinning spheres, each rotating 'counter-clockwise' with the moon itself orbiting the Earth in a 'counter-clockwise' direction as well (and at such an orbital rate — relative to its own axial rotation — that the same side always faces the earth). So looking down from a fixed point in space above the north pole the Apollo (and all other manned spacecraft before and since) launched into a 'counter-clockwise' orbit. The moon is orbiting 'counter-clockwise' as well but the mission insignia/figure 8 would have one believe that the Apollo lunar orbit was clockwise (i.e. east-to-west). It actually goes beyond the mission patch (which I recognize was only cleverly representative of the mission, incorporating the number '8'). This famous John Houbolt diagram seems to also indicate that the lunar trajectory was a 'figure 8' and the Apollo lunar orbit was opposite in direction to that of the Earth orbit (and hence opposite to the moon's own axial rotation). It would seem to me that Apollo would have wanted to orbit the moon in the same direction the moon was turning (which is the same as the Earth) to take advantage of its motion when the LM ascent stage launched. But that would not give the 'figure 8' profile shown in the diagrams. Any FIDOs or GUIDANCEs out there? |
pterodactyl Member Posts: 21 From: Registered: Feb 2006
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posted 12-21-2007 02:32 PM
One explanation might be that the small rotation rate of the Moon (one rotation every 28 days) did not impart sufficient 'delta vee' to be of significance to gaining lunar orbit. The energy savings of the "figure 8" free return profile likely trumped those considerations. |
pterodactyl Member Posts: 21 From: Registered: Feb 2006
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posted 12-21-2007 03:19 PM
As an addition to the above statement a rough calculation of the contribution of lunar rotation (at the lunar equator) gave the following:4.56 meters/sec or ~15 ft/sec or ~ 10 mph. Pretty small compared to the 'delta vee' contribution of the Earth's rotation which is the result of a significantly larger body rotating about 28X as fast. |
Robert Pearlman Editor Posts: 43576 From: Houston, TX Registered: Nov 1999
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posted 12-21-2007 03:45 PM
I'm not sure if this will help answer the question, but I've recorded a short movie (Quicktime, 640kb) with the help of Starry Night Apollo that illustrates the trajectory followed by Apollo 8 from a perch beyond the Moon, looking back at the Earth. The movie starts just before Apollo 8 entered lunar orbit and ends just after departing the Moon.As a point of comparison, here is an additional movie (1.2mb) showing Apollo 13's 'figure 8' trajectory. |
John Charles Member Posts: 342 From: Houston, Texas, USA Registered: Jun 2004
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posted 12-21-2007 10:40 PM
quote: Originally posted by pterodactyl: Pretty small compared to the 'delta vee' contribution of the Earth's rotation...
In addition to the previous clarifications, also note that a trajectory from Earth to the moon that results in a clockwise (as seen from above the moon's north pole) lunar orbit requires slightly less energy leaving the Earth than does an orbit in the opposite direction. The Apollo-style clockwise trajectory is in the form of a high Earth orbit that falls slightly short of reaching the moon, which then uses the moon's gravity to pull it the rest of the way. A counterclockwise lunar orbit would require a trajectory that carries the vehicle beyond the moon, which would start out as an even higher Earth orbit, which would require more energy on departure.There are probably other dynamical reasons for the trajectory decision as well. |
Paul78zephyr Member Posts: 678 From: Hudson, MA Registered: Jul 2005
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posted 12-22-2007 09:19 PM
Thank you to all! That information is very interesting, and (interestingly enough as it is) quite scarce. In the time since I posted my original question I searched online and through the many Apollo/spaceflight historical books that I own. Many of them show the John Houbolt diagram (or a similar NASA diagram) but no where did I read any reason given for the figure 8 trajectory that was, apparently, utilized. I'm sure the way it was done was the most efficient way from a total mission standpoint taking into effect both earth and lunar gravity. The fact that the moons axial rotation is quite slow and would yield only a small velocity advantage is appreciated — I only thought that with NASA/Grumman literally trying the slim the LM by ounces it would have seemed reasonable that they would take advantage of even a slight gain from the rotational velocity of the lunar surface. In thinking about it I also thought, perhaps, that an east-to-west lunar orbit would have some lighting advantage during the critical landing and takeoff phases, but I did not read anything about that. I wonder if the future Orion missions are being planned with the same type of figure 8 trajectory as used on Apollo? |
John Charles Member Posts: 342 From: Houston, Texas, USA Registered: Jun 2004
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posted 12-22-2007 10:02 PM
quote: Originally posted by Paul78zephyr: I wonder if the future Orion missions are being planned with the same type of figure 8 trajectory as used on Apollo?
All the analyses I have seen show the same type of figure-8 trajectory. |
Rocketman! Member Posts: 122 From: Redmond, Washington, USA Registered: Dec 2007
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posted 12-22-2007 11:03 PM
Seeing this discussion has compelled me to finally register as a collectSPACE member. I stumbled upon this discussion by way of a search for Starry Night Apollo. I hope you don't mind me putting in my two cents worth.I'll say up front that I'm no expert in this subject, but my background in science, engineering, and teaching astronomy and space subjects should serve to give you some confidence in my answer. I find the topic of spaceflight trajectories and rendezvous very interesting. It is my understanding that the Apollo flights to the Moon did, indeed, follow a "Figure-8" path... relative to the Earth-Moon frame of reference. The image link provided by Paul is more representative, because it shows the effect of the Moon's travel in its orbit. But, you can see that neglecting the Moon's travel (as I say, in the Earth-Moon frame of reference), the path looks like a "Figure-8." The reasons for this, as I have observed over the years, are as follows: - WEIGHT SAVINGS - The primary reason is to save fuel, and therefore reduce weight of the spacecraft. I'm sure you've heard of the "slingshot" maneuver. The Voyager spacecraft are probably the most notable for using this trajectory that uses a planet's gravity to accelerate itself and change direction for its next destination. An easy-to-read scientific explanation is here. On the second page of the explanation, the figures show how this is done.
In the case of the Apollo spacecraft, the reverse of this was done to reduce the speed of the spacecraft so that less fuel would be needed to slow the spacecraft into lunar orbit. This was done, as I understand it, by approaching the Moon on its advancing (West) side, and thus entering a "clockwise" lunar orbit. Again, referring to the diagrams on the JPL web site, the orbital motion of the Moon was essentially subtracted from the velocity of the spacecraft, instead of added to it as in the case of Voyager. So, there was less thrust needed from the Apollo Service Module propulsion system, which translates to less fuel needed, which translates to a lighter spacecraft and a lighter overall rocket and its associated fuel. - SUN ANGLE - I recall accounts from the astronauts saying that they didn't see the Moon until they were in lunar orbit because they were in the Moon's shadow. I also recall that the landings were done during the Moon's first quarter phase.
So, how does this support the "Figure-8" theory? Bear with me... They also wanted to approach the landing site in the final phase of descent with the Sun behind them at a very low angle. Behind so the sun wasn't in their eyes, and low so the long shadows would provide clear visual cues to the nature of the terrain. Putting this all together supports the "Figure-8"/clockwise lunar orbit hypothesis as follows... Picture the Earth-Moon system from "above" the North Pole. Put the Earth in the center of the "clock" and the Moon in the "12 o'clock" position. Put the Sun on the extreme right of the picture, illuminating the Earth's and Moon's right sides. The shadows of the Earth and Moon trail off to the left. The Moon's phase in this configuration is the first quarter. Apollo launches from the Earth in a "counter-clockwise" direction to take advantage of the speed of the Earth's rotation (as correctly mentioned by a previous poster). The Apollo spacecraft approaches the Moon on the advancing (or West) side - the left side on our imaginary drawing. The spacecraft is in the shadow of the Moon, and thus the Moon cannot be easily seen except for some amount of reflected Earthshine. As Apollo 8 neared its target, the spacecraft was turned so that its rocket engine pointed into the direction of flight. Bill Anders would later describe how he first became aware of the moon, as the spacecraft moved into the shadowed region where neither sunlight nor reflected light from Earth was visible -- what the astronauts called the "double umbra." As Anders recalled, "Suddenly, we saw millions of stars, more than you could see in a planetarium, to the point where it confused the constellations. So that was rather spectacular. And I remember looking at them because I was interested in astronomy, and then I looked kind of over my left shoulder and suddenly, the stars stopped. And there was this big black void, black hole. And that was the moon! That was the moon shielding the stars and yet not illuminated. It was as black as I've ever seen black. That was the only time in the flight the hair kind of came up on the back of my neck a little bit." [Source] Apollo enters lunar orbit in a "clockwise" direction, expending a smaller amount of fuel because of the "reverse slingshot" effect. On the far side of the Moon, the Apollo astronauts cross the terminator and get their first close-up look at the sunlit side of the Moon. ("... a vast, lonely, forbidding type of existence or expanse of nothing ..." - Frank Borman, Apollo 8) It is their first lunar "sunrise". Several minutes later, as they come around the East (right) limb of the Moon, they see their first lunar "Earthrise"!Another collectSPACE discussion notes that in the famous Apollo 8 image [Source], "North" is to the right. This supports the "clockwise" lunar orbit theory, as well. Apollo 11 took it the rest of the way. It's final descent brought it down to the landing spot [Source], moving from right to left as viewed from Earth. The Sun was at their backs and the long shadows fell away ahead of them until overtaken completely past the terminator. Lunar take-off and rendezvous were in the same "clockwise" direction, as was trans-Earth injection. Finally, although I know of no references that say so, I believe the re-entry into Earth's atmosphere was in a "counter-clockwise" direction, just as was the case for the lift-off from Earth. I think it would make sense to re-enter in the direction of the Earth's rotation to minimize the relative speed between the spacecraft and the atmosphere.(I hope you enjoyed reading this as much as I did writing it.) |
Rocketman! Member Posts: 122 From: Redmond, Washington, USA Registered: Dec 2007
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posted 12-23-2007 01:01 AM
Additional resources:I remember, as a kid, having a 4-foot long poster with the Apollo trajectory milestones illustrated. I was curious to see what I could find with a quick image search on Google. Here's what I came up with... Note on this image [Source, also see this], the dotted line showing the "slingshot" trajectory used to accelerate the S-IVB third stage into a solar orbit. On this figure [Source], note the green dashed "free return" trajectory... also shown as a "Figure-8." |
John Charles Member Posts: 342 From: Houston, Texas, USA Registered: Jun 2004
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posted 12-23-2007 11:24 AM
quote: Originally posted by Rocketman!: They also wanted to approach the landing site in the final phase of descent with the Sun behind them at a very low angle. Behind so the sun wasn't in their eyes, and low so the long shadows would provide clear visual cues to the nature of the terrain...
Of course, the desired low sun angle at landing could also have been accommodated if Apollo had entered a counterclockwise lunar orbit, simply by delaying launch and subsequent arrival at the moon by two weeks (half of a lunar solar day). However, in that case, it would have gotten closer to sunset the longer the crew stayed on the moon, and EVAs would have had to contend with lengthening, inky-black shadows obscuring surface features. Apollo actually benefited from shortening shadows as the sun rose higher during the 3-(Earth)day stays, improving surface feature visibility. |
Rocketman! Member Posts: 122 From: Redmond, Washington, USA Registered: Dec 2007
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posted 12-23-2007 12:36 PM
John makes a very good, and I believe correct point. (My post was getting a little long, so thanks for completing the details.) Nobody wanted to be stranded on the Moon in the dark if there was an unexpected delay. And during the extended stays on the surface on the later Apollo missions, the setting sun of a last quarter phase would have complicated things even further. |
LM-12 Member Posts: 3324 From: Ontario, Canada Registered: Oct 2010
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posted 12-30-2015 12:39 PM
In the Apollo 8 mission insignia, the plane of the figure-8 trajectory of the spacecraft is shown parallel to the plane of the Earth's equator. But on the actual mission, the plane of the figure-8 trajectory was parallel to the plane of the moon's orbit around the Earth. That is a tilt of about 28 degrees from the plane of the Earth's equator. Is that correct? |
moonguyron Member Posts: 191 From: Trinity, FL USA Registered: Jan 2011
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posted 12-30-2015 07:48 PM
At the risk of interjecting more questions than I resolve, shouldn't that be 23.5 degrees? Somebody help me here but it is my understanding, admittedly relying on deficient grade school planetary geometry, that the reason for the launch angle for Apollo was to compensate for this 23 degree tilt and to get the spacecraft in earth orbit to more echo the plane of the moon's orbit. Launching at a declination of 72 degrees east of north would, for instance, negate 18 degrees of the earths tilt. Depending then on the time of year (season) this would be sufficient put the spacecraft in an orbital plane in earth orbit that matches essentially the plane of the moon's orbit. Right? |
moorouge Member Posts: 2458 From: U.K. Registered: Jul 2009
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posted 12-31-2015 01:29 AM
quote: Originally posted by Paul78zephyr: The moon is orbiting 'counter-clockwise' as well but the mission insignia/figure 8 would have one believe that the Apollo lunar orbit was clockwise (i.e. east-to-west).
This assumes that the Moon orbits the Earth as seen from a fixed point in space. The actual path of the Moon round the Earth is more like this - |
LM-12 Member Posts: 3324 From: Ontario, Canada Registered: Oct 2010
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posted 12-31-2015 09:14 AM
Here is a diagram that shows the plane of the Earth's equator and the plane of the translunar trajectory. |
canyon42 Member Posts: 238 From: Ohio Registered: Mar 2006
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posted 12-31-2015 09:57 AM
The diagram posted by moorouge is only "sort of" correct. Yes, the moon swings from one side of the Earth to the other during its orbit; however, the incorrect scale of the diagram gives an inaccurate impression of the directional changes involved. In fact, if you accurately scale both the Earth-moon orbit around the sun and the moon's orbit around the Earth, the moon's yearly path around the sun is always concave. There is just a slight difference in the degree of concavity at the times of full and new moons. |
moorouge Member Posts: 2458 From: U.K. Registered: Jul 2009
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posted 01-02-2016 02:23 AM
If one is going to be very picky and pedantic about the orbital paths of satellites then one needs to specify the reference point used to define the orbit. From a heliocentric viewpoint the Apollo lunar flights became satellites of the Moon as it followed its path round the Sun. Consequently, Apollo 8's path round the Moon is as described in my diagram to show the Moon's orbit round the Earth, simply substitute the Moon for the Earth and Apollo 8 for the Moon. It all makes it even more incredible that the computers used on Apollo - knitted together by the women of Raytheon - were capable of solving the complex equations required to compute the flight paths for the Apollo lunar missions. |
canyon42 Member Posts: 238 From: Ohio Registered: Mar 2006
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posted 01-02-2016 09:22 AM
It's not a matter of being "picky and pedantic," it's a simple matter of scale. If you "stretch" the Earth/moon system's orbit around the sun to its true scale, both the Earth and the moon travel paths that are very nearly identical to circles. As I noted, yes, the moon's orientation *in relation to the Earth* does have it alternating from one side to the other. However, the diagram makes it appear that the moon swings fairly dramatically toward and away from the sun as it travels around the Earth, and that just doesn't happen.My post was not intended as a criticism, just a clarification of the "real" situation. It is in fact impossible to make a practical diagram of the type you posted that is properly in scale, at least one of a size that would fit on a computer screen--the minuscule sizes of the objects involved compared to the immensity of their orbits means that they are literally specks that are indistinguishable from dust on the screen. That's a point that we make each year with my elementary school science club, as we build a model of our solar system starting with the sun as a basketball. At that scale the Earth is a dot something like a quarter-inch wide that is about 30 yards from the basketball. (Actually, I should say we build a model of *part* of the solar system--our schoolyard is a large one, but we run out of room just short of reaching Saturn, and have to make reference to public buildings in our town to "place" Uranus, Neptune, and Pluto.) |
LM-12 Member Posts: 3324 From: Ontario, Canada Registered: Oct 2010
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posted 01-02-2016 10:06 AM
quote: Originally posted by moonguyron: shouldn't that be 23.5 degrees?
There is a third plane involved: the plane of the Earth's orbit around the Sun. Another diagram shows 23.5 degrees as the angle between the plane of the Earth's equator, and the plane of the Earth's orbit around the Sun. |
moonguyron Member Posts: 191 From: Trinity, FL USA Registered: Jan 2011
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posted 01-02-2016 04:03 PM
So, referring to the diagram posted above by LM-12, what is the angle between the spacecraft's earth orbital plane (which corresponds with the moon's orbital plane) and the equator? And is it always the same and not dependent on the launch window date? |
LM-12 Member Posts: 3324 From: Ontario, Canada Registered: Oct 2010
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posted 01-02-2016 10:12 PM
Based on the diagrams I have seen, that angle is 28.65 degrees. |
LM-12 Member Posts: 3324 From: Ontario, Canada Registered: Oct 2010
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posted 01-03-2016 10:42 AM
The transearth trajectory sure doesn't look right in the Apollo Program insignia. |
moonguyron Member Posts: 191 From: Trinity, FL USA Registered: Jan 2011
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posted 01-07-2016 08:05 PM
An in-depth explanation of the physics of Apollo moon bound launches can be found by doing a search for "Launch Windows Essay". This is put out by the NASA history office and explains launch angles relative to the earth and moon and other launch constraints. |